Appears in collection : Summer School 2016 - Geometric Analysis, Metric Geometry and Topology

We study sequences of closed minimal hypersurfaces (in closed Riemannian manifolds) that have uniformly bounded index and area. In particular, we develop a bubbling result which yields a bound on the total curvature along the sequence. As a consequence, we obtain qualitative control on the topology of minimal hypersurfaces in terms of index and area. This is joint work with Ben Sharp.